Question

对任意实数x,y,求S=x^2+2xy+3y^2+2x+6y+4的最小值

Answer 1

S=x^2+2xy+3y^2+2x+6y+4

S=(x+y)^2+2x+2y+1+2y^2+4y+3

S=(x+y)^2+2(x+y)+1+2(y+1)^2+1

S=(x+y+1)^2+2(y+1)^2+1>=1

当x+y+1=0

且y+1=0的时候,S取最小值1

即x=0,y=-1时,S最小为1